What is (2log_{3}(5))/(log_{3)(4)} ?

The solution to (2log_{3}(5))/(log_{3)(4)} is log_{2}(5)

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simplify (2log_{3}(5))/(log_{3)(4)}

simplify

\frac{2 lo g _{3} ( 5 )}{lo g _{3} ( 4 )}

lo g_{2} (5)

Decimal Notation

2.32192 \dots

Solution steps

\frac{2 lo g _{3} ( 5 )}{lo g _{3} ( 4 )}

Apply log rule:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{lo g _{3} ( 5 )}{lo g _{3} ( 4 )} = lo g_{4} (5)

= 2 lo g_{4} (5)

Factor the number:

4 = 2^{2}

= 2 lo g_{2^{2}} (5)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{2}} (5) = \frac{1}{2} lo g_{2} (5)

= 2 \cdot \frac{1}{2} lo g_{2} (5)

2 \cdot \frac{1}{2} lo g_{2} (5) = lo g_{2} (5)

= lo g_{2} (5)

32 \cdot 9

(x + y + 2)^{2}

x^{2} - 2 a x + a^{2}

\frac{1}{lo g _{8} ( 2 )}

(5 x^{3} + 4 x^{2}) - (6 x^{2} - 2 x - 9)

What is (2log_{3}(5))/(log_{3)(4)} ?
The solution to (2log_{3}(5))/(log_{3)(4)} is log_{2}(5)